SECT, xvii.] VIBRATION OF LAMINA. 163 



caused the sand to form in lines perpendicular to the first 

 had the plate been at rest, the combined vibrations will- 

 make the sand form in lines from corner to corner (N. 180). 



M. Savart's experiments on the vibrations of flat glass 

 rulers are highly interesting. Let a lamina of glass 27 in> 56 

 long, 0'59 of an inch broad, and O06 of an inch in thick- 

 ness, be held by the edges in the middle, with its flat surface 

 horizontal. If this surface be strewed with sand, and set in 

 longitudinal vibration by rubbing its under surface with a wet 

 cloth, the sand on the upper surface will arrange itself in 

 lines parallel to the ends of the lamina, always in one or other 

 of two systems (N. 181). Although the same one of the 

 two systems will always be produced by the same plate of 

 glass, yet among different plates of the preceding dimensions, 

 even though cut from the same sheet side by side, one will 

 invariably exhibit one system, and the other the other, 

 without any visible reason for the difference. Now, if the 

 positions of these quiescent lines be marked on the upper 

 surface, and if the plate be turned so that the lower surface 

 becomes the upper one, the sand being strewed, and vibrations 

 excited as before, the nodal lines will still be parallel to the 

 ends of the lamina, but their positions will be intermediate 

 between those of the upper surface (N. 182). Thus it ap- 

 pears that all the motions of one half of the thickness of the 

 lamina, or ruler, are exactly contrary to those of the corre- 

 sponding points of the other half. If the thickness of the la- 

 mina be increased, the other dimensions remaining the same, 

 the sound will not vary, but the number of nodal lines will 

 be less. When the breadth of the lamina exceeds the 0'6 of 

 an inch, the nodal lines become curved, and are different on 

 the two surfaces. A great variety of forms are produced by 

 increasing the breadth and changing the form of the sur- 

 face ; but in all it appears that the motions in one half of 

 the thickness are opposed to those in the other half. 



M. Savart also found, by placing small paper rings round 

 a cylindrical tube or rod, so as to rest upon it at one point 



M 2 



